Rikkupikku
A good option for backpackers
This has a very central location, close to all the city's services. They have free wifi, tea and coffee, and if you ask, the managers will give you the chance to join their organised trips and excursions. The price is fantastic, around 20 euros for one night, with breakfast included. There are rooms from 2-12 people, so if you want to visit Bilbao with a group of friends, this is a good choice. They have heating and security cards, bunk beds, and storage lockers for your luggage.